The generator matrix

 1  0  1  1  1  0  1 X^2+X  1  1 X^2+X  1  1 X^2  1  1  0  1  1  X  1  1  1 X^2+X  1 X^2+X  1  1  1  1  X  1  1  X  1 X^2+X  1  1  1  0  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  X  1  1  0  1  1  1  1  1  1  0 X^2  1  1  1  1  1  1  1  0 X^2+X
 0  1  1  0 X^2+X+1  1  X  1 X^2+X+1  X  1  1 X^2  1 X+1 X^2+X  1 X+1  0  1  X X+1  1  1  1  1 X^2+1  X X^2 X+1  1 X+1 X^2+X+1  1  0  1 X^2+1  1 X^2  1  1 X^2+X+1 X^2+X X^2+1 X^2+1  1 X^2 X^2+X X^2+X X^2+X X^2+X  1 X+1 X^2+1 X^2+X  1 X^2+X  1  1 X^2+1 X^2+X+1 X+1 X+1 X^2+X+1  1  1  1  X X^2+X X^2+1 X+1 X^2+X+1  1  X  X  1
 0  0  X  0 X^2+X  X  0  X  0  X  0 X^2 X^2+X  X  X  X  0 X^2  X X^2+X X^2 X^2 X^2+X X^2  0 X^2+X X^2  0 X^2+X X^2  X  X X^2 X^2+X X^2  0  X  0  0 X^2 X^2 X^2+X X^2+X X^2+X X^2+X  0 X^2+X  0  X X^2 X^2+X X^2+X  0  X X^2+X  X  0  X X^2+X X^2 X^2+X X^2 X^2  X  0  0 X^2+X X^2  0  X X^2+X  X  0 X^2+X  0  0
 0  0  0  X  0  X  X  X X^2+X  0 X^2  X X^2 X^2 X^2+X  X  X  0 X^2+X X^2  0 X^2+X  0 X^2+X X^2  X X^2 X^2+X X^2  X X^2  X X^2+X X^2  0  0 X^2+X  0 X^2+X X^2+X  X  0  0 X^2  X X^2  X  0 X^2 X^2 X^2+X X^2+X X^2  X X^2 X^2+X X^2 X^2 X^2+X X^2+X  X X^2 X^2  X  0 X^2+X  0 X^2+X X^2+X  X X^2 X^2 X^2+X  0 X^2  0
 0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0  0 X^2

generates a code of length 76 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+132x^70+132x^71+239x^72+116x^73+215x^74+116x^75+225x^76+104x^77+206x^78+124x^79+140x^80+164x^81+71x^82+12x^83+13x^84+12x^86+16x^88+4x^90+4x^92+1x^104+1x^112

The gray image is a linear code over GF(2) with n=304, k=11 and d=140.
This code was found by Heurico 1.16 in 0.527 seconds.